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arxiv: 2605.02685 · v2 · submitted 2026-05-04 · ❄️ cond-mat.mtrl-sci

Recognition: 3 theorem links

· Lean Theorem

A Unified microscopic picture of cation and anion migration in MAPbI₃

Viren Tyagi , Geert Brocks , Shuxia Tao
Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:55 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords MAPbI3ion migrationhybrid perovskitesdefect diffusionMA interstitialsneural network potentialsmolecular dynamicsconcerted motion
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The pith

MA interstitials migrate rapidly in MAPbI3 through concerted motion of multiple molecules, alongside fast diffusion of iodine defects.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Molecular dynamics simulations driven by neural network potentials trained on DFT data show that most point defects in MAPbI3, such as iodine vacancies and interstitials plus MA interstitials, move quickly at room temperature with barriers of 0.15 to 0.20 eV. MA interstitials achieve this speed via a concerted process in which several MA molecules shift together, while MA vacancies show no migration. Iodine defect mobility varies with charge state but MA defect mobility does not. These paths revise the usual emphasis on isolated iodine ions alone and indicate that collective organic-cation motion drives the high ionic conductivity observed in the material.

Core claim

In MAPbI3, I-related defects and MA interstitials exhibit rapid diffusion at room temperature with migration barriers between 0.15 and 0.20 eV. MA interstitials move through a concerted mechanism involving multiple MA ions. No evidence appears for MA vacancy migration. Diffusion of I defects depends on charge state, while MA defect diffusion does not. These results revise the conventional picture of ion transport in hybrid perovskites.

What carries the argument

Concerted migration mechanism of multiple MA ions, revealed in long-timescale MD trajectories, that allows MA interstitials to achieve low barriers despite their molecular size.

If this is right

  • Passivation and mobility-restriction strategies must target both iodine and methylammonium defects to improve perovskite device lifetimes.
  • The absence of MA vacancy migration implies that certain cation defects remain more stable and less mobile than models focused only on iodine would predict.
  • Charge-state dependence for iodine defects but not for MA defects allows selective control of anion versus cation transport through doping or electric bias.
  • Organic-cation dynamics must be included in any model that aims to predict or suppress unwanted ion migration in hybrid perovskites.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same concerted mechanism may appear in other hybrid perovskites with different organic cations, offering a general route to fast ionic transport.
  • Device-scale transport measurements could be reinterpreted to include significant contributions from MA interstitials rather than iodine defects alone.
  • Neural-network-potential MD can be extended to study defect-defect interactions or higher defect concentrations that are inaccessible to direct DFT.

Load-bearing premise

The neural network potentials trained on DFT data accurately capture the energy barriers and mechanisms for defect migration across the relevant charge states and timescales.

What would settle it

An experiment or higher-accuracy calculation that measures the activation energy for MA interstitial diffusion and obtains a value well above 0.20 eV, or that shows isolated rather than concerted MA ion motion.

Figures

Figures reproduced from arXiv: 2605.02685 by Geert Brocks, Shuxia Tao, Viren Tyagi.

Figure 1
Figure 1. Figure 1: Energies along the NEB migration paths, calculated using DFT and the NNPs. The points are the calculated values, and the lines guide the eye; the energy of the minima is set to 0. The forces calculated using the NNP are also compared with those calculated using DFT. This is done using structures sampled from MD simu￾lations at 600 K performed on 6×6×6 supercells of MAPbI3 (2592 atoms) with one I or MA poin… view at source ↗
Figure 2
Figure 2. Figure 2: Temperature-dependent diffusion coef￾ficients of iodide interstitial (I− I ), iodide vacancy (V+ I ), neutral MA interstitial (I0 MA), and positive MA interstitial (I+ MA) defects in MAPbI3 . The dashed lines represent the fits to an Arrhenius ex￾pression, and the error bars represent the standard error in mean at each point. For all defects the temperature dependence of the diffusion coefficient can be fi… view at source ↗
Figure 3
Figure 3. Figure 3: Schematic representation of the diffusion of the MA interstitial. The red arrows represent the view at source ↗
read the original abstract

Passivating defects and restricting defect mobilities in halide perovskites to increase device lifetimes has become a main field of research. Modeling structure and mobility of point defects is an essential contribution to this endeavor. We employ molecular dynamics, based on neural network potentials trained on density functional theory data, to model ion migration in MAPbI$_3$ triggered by I and MA vacancies or interstitials. Most of these species diffuse rapidly at room temperature, with migration barriers between 0.15 and 0.20 eV. MA interstitials are highly mobile despite their molecular nature, owing to a concerted migration mechanism involving multiple MA ions. No evidence of MA vacancy migration is obtained. Whereas diffusion of I-related defects appreciably depends on their charge state, diffusion of MA defects does not. These results revise the conventional picture of ion transport in hybrid perovskites and highlight the role of collective molecular motion in enabling fast ionic migration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript employs molecular dynamics simulations based on neural network potentials trained on DFT data to model the migration of iodine and methylammonium (MA) vacancies and interstitials in MAPbI₃. It reports low migration barriers (0.15–0.20 eV) for most defects at room temperature, a concerted multi-ion mechanism for highly mobile MA interstitials, absence of MA vacancy migration, and charge-state dependence in diffusion for I-related defects but not MA defects. These findings are presented as revising the conventional picture of ion transport in hybrid perovskites by emphasizing collective molecular motion.

Significance. If the NN potentials accurately reproduce the relevant energy landscapes for charged defects and collective MA displacements, the work would provide a valuable unified microscopic view of cation and anion migration, highlighting how concerted motions enable fast ionic diffusion. This could inform defect passivation strategies for improving perovskite device lifetimes. The use of ML potentials to access longer timescales than direct DFT-MD is a methodological strength for observing rare events.

major comments (3)
  1. [Methods] Methods section on NN potential training and validation: No independent benchmarks (such as NEB-computed barriers or force errors on charged defect supercells) are reported for the migration saddle points of I and MA defects in different charge states. Since the central claims of low barriers (0.15–0.20 eV) and the concerted MA interstitial mechanism rest entirely on the MD trajectories, this validation is load-bearing and its absence leaves open the possibility that observed features are potential artifacts.
  2. [Results] Results on MA vacancy migration: The conclusion of 'no evidence of MA vacancy migration' is drawn from MD trajectories, but without reported details on total simulation time, number of independent runs, or statistical sampling of rare events, it is unclear whether this reflects a truly high barrier or insufficient sampling. This directly affects the claim of differential behavior between MA interstitials and vacancies.
  3. [Results] Description of concerted MA interstitial mechanism: The collective multi-ion motion is invoked to explain high mobility, yet the manuscript provides only qualitative trajectory descriptions without quantitative metrics (e.g., ion-ion displacement correlations or coordination changes at the saddle point). This detail is essential to substantiate the revision of the conventional single-ion hop picture.
minor comments (2)
  1. [Abstract] Abstract: The charge states explicitly simulated for each defect species (vacancy/interstitial, I/MA) should be stated to allow immediate assessment of the scope of the charge-state dependence claims.
  2. [Figures] Figures: Energy profiles or trajectory snapshots would benefit from explicit labeling of charge states and simulation temperatures to improve clarity when comparing I and MA defect behaviors.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments. We address each major point below and have revised the manuscript to strengthen the validation, reporting, and quantitative support for our claims.

read point-by-point responses

  1. Referee: [Methods] Methods section on NN potential training and validation: No independent benchmarks (such as NEB-computed barriers or force errors on charged defect supercells) are reported for the migration saddle points of I and MA defects in different charge states. Since the central claims of low barriers (0.15–0.20 eV) and the concerted MA interstitial mechanism rest entirely on the MD trajectories, this validation is load-bearing and its absence leaves open the possibility that observed features are potential artifacts.

    Authors: We agree that explicit validation of the NN potential on the relevant saddle points is important. In the revised manuscript we have added NEB calculations performed with the trained NN potential for the key I and MA defect migration paths in the relevant charge states. Where computationally feasible we also compare selected NN-NEB barriers directly to DFT-NEB results. In addition, we report the force errors of the NN model on an independent test set of charged defect supercell configurations. These benchmarks confirm that the low barriers and concerted mechanisms observed in the MD trajectories are reproduced by the NN potential and are not artifacts. revision: yes

  2. Referee: [Results] Results on MA vacancy migration: The conclusion of 'no evidence of MA vacancy migration' is drawn from MD trajectories, but without reported details on total simulation time, number of independent runs, or statistical sampling of rare events, it is unclear whether this reflects a truly high barrier or insufficient sampling. This directly affects the claim of differential behavior between MA interstitials and vacancies.

    Authors: We acknowledge that additional protocol details are required. The revised manuscript now reports the total accumulated simulation time (several hundred nanoseconds across all trajectories), the number of independent runs started from different initial configurations, and a brief discussion of the sampling statistics. No MA vacancy hops were observed in any run, while interstitial and I-related defects diffused readily on the same timescale. This differential behavior is therefore unlikely to be due to insufficient sampling and supports our conclusion of a substantially higher barrier for MA vacancies. revision: yes

  3. Referee: [Results] Description of concerted MA interstitial mechanism: The collective multi-ion motion is invoked to explain high mobility, yet the manuscript provides only qualitative trajectory descriptions without quantitative metrics (e.g., ion-ion displacement correlations or coordination changes at the saddle point). This detail is essential to substantiate the revision of the conventional single-ion hop picture.

    Authors: We agree that quantitative characterization strengthens the mechanistic claim. In the revised manuscript we have added ion-ion displacement correlation functions computed from the MD trajectories, together with a description of the changes in MA coordination and Pb-I framework geometry at the identified saddle points. These metrics demonstrate clear concerted displacement of multiple MA ions during interstitial migration, providing quantitative support for the departure from the conventional single-ion hop picture. revision: yes

Circularity Check

0 steps flagged

No significant circularity; results are simulation outputs from externally trained potentials.

full rationale

The paper trains neural network potentials on DFT data (external to the paper) and then performs MD simulations to extract migration barriers and mechanisms for defects in MAPbI3. The central claims (low barriers 0.15-0.20 eV, concerted MA interstitial motion, charge-state dependence differences, absence of MA vacancy migration) are direct outputs of those trajectories, not reductions of the training data or fitted parameters by construction. No self-definitional equations, no renaming of fitted quantities as predictions, and no load-bearing self-citations that close the derivation loop are present in the provided abstract or described methodology. The derivation chain remains open to external validation via the underlying DFT and the MD sampling.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claims rest on the accuracy of NN potentials fitted to DFT for describing defect energetics and on standard assumptions of classical MD for capturing migration events at room temperature.

free parameters (1)
  • Neural network potential parameters
    Fitted to DFT energies and forces to enable large-scale MD; specific values and training details not provided in abstract.
axioms (2)
  • domain assumption The NN potential reproduces DFT-level barriers and forces sufficiently for qualitative and semi-quantitative migration behavior.
    Invoked to justify using the potentials for MD trajectories of charged defects.
  • domain assumption Periodic boundary conditions and simulation cell sizes do not artificially constrain the observed concerted mechanisms.
    Standard for MD but critical for collective motions involving multiple MA ions.

pith-pipeline@v0.9.0 · 5462 in / 1348 out tokens · 35035 ms · 2026-05-08T17:55:53.384999+00:00 · methodology

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Reference graph

Works this paper leans on

76 extracted references · 56 canonical work pages

  1. [1]

    Tyagi, Viren and Pols, Mike and Brocks, Geert and Tao, Shuxia , title =. J. Phys. Chem. Lett. , volume =. 2025 , doi =

    2025

  2. [2]

    Whitfield, P. S. and Herron, N. and Guise, W. E. and Page, K. and Cheng, Y. Q. and Milas, I. and Crawford, M. K. , title=. Sci. Rep. , year=. doi:10.1038/srep35685 , url=

    work page doi:10.1038/srep35685

  3. [3]

    On representing chemical environments , author =. Phys. Rev. B , volume =. 2013 , month =. doi:10.1103/PhysRevB.87.184115 , url =

    work page doi:10.1103/physrevb.87.184115 2013

  4. [4]

    Gaussian Approximation Potentials: The Accuracy of Quantum Mechanics, without the Electrons , author =. Phys. Rev. Lett. , volume =. 2010 , month =. doi:10.1103/PhysRevLett.104.136403 , url =

    work page doi:10.1103/physrevlett.104.136403 2010

  5. [5]

    Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set , author =. Phys. Rev. B , volume =. 1996 , month =. doi:10.1103/PhysRevB.54.11169 , url =

    work page doi:10.1103/physrevb.54.11169 1996

  6. [6]

    On-the-fly machine learning force field generation: Application to melting points , author =. Phys. Rev. B , volume =. 2019 , month =. doi:10.1103/PhysRevB.100.014105 , url =

    work page doi:10.1103/physrevb.100.014105 2019

  7. [7]

    Phase Transitions of Hybrid Perovskites Simulated by Machine-Learning Force Fields Trained on the Fly with Bayesian Inference , author =. Phys. Rev. Lett. , volume =. 2019 , month =. doi:10.1103/PhysRevLett.122.225701 , url =

    work page doi:10.1103/physrevlett.122.225701 2019

  8. [8]

    Crystal Structure and Pair Potentials: A Molecular-Dynamics Study , author =. Phys. Rev. Lett. , volume =. 1980 , month =. doi:10.1103/PhysRevLett.45.1196 , url =

    work page doi:10.1103/physrevlett.45.1196 1980

  9. [9]

    and Rahman, A

    Parrinello, M. and Rahman, A. , title =. J. Appl. Phys. , volume =. 1981 , month =

    1981

  10. [10]

    From ultrasoft pseudopotentials to the projector augmented-wave method , author =. Phys. Rev. B , volume =. 1999 , month =. doi:10.1103/PhysRevB.59.1758 , url =

    work page doi:10.1103/physrevb.59.1758 1999

  11. [11]

    Strongly Constrained and Appropriately Normed Semilocal Density Functional , author =. Phys. Rev. Lett. , volume =. 2015 , month =. doi:10.1103/PhysRevLett.115.036402 , url =

    work page doi:10.1103/physrevlett.115.036402 2015

  12. [12]

    Nonlocal van der Waals density functional made simple and efficient , author =. Phys. Rev. B , volume =. 2013 , month =. doi:10.1103/PhysRevB.87.041108 , url =

    work page doi:10.1103/physrevb.87.041108 2013

  13. [13]

    First-principles calculations of defects in metal halide perovskites: A performance comparison of density functionals , author =. Phys. Rev. Mater. , volume =. 2021 , month =. doi:10.1103/PhysRevMaterials.5.125408 , url =

    work page doi:10.1103/physrevmaterials.5.125408 2021

  14. [14]

    Finite-temperature structure of the

    Lahnsteiner, Jonathan and Kresse, Georg and Heinen, Jurn and Bokdam, Menno , journal =. Finite-temperature structure of the. 2018 , month =. doi:10.1103/PhysRevMaterials.2.073604 , url =

    work page doi:10.1103/physrevmaterials.2.073604 2018

  15. [15]

    Assessing Density Functionals Using Many Body Theory for Hybrid Perovskites , author =. Phys. Rev. Lett. , volume =. 2017 , month =. doi:10.1103/PhysRevLett.119.145501 , url =

    work page doi:10.1103/physrevlett.119.145501 2017

  16. [16]

    Special points for Brillouin-zone integrations , author =. Phys. Rev. B , volume =. 1976 , month =

    1976

  17. [17]

    Andreas Bender, Nadine Schneider, Marwin Segler, W

    Batzner, Simon and Musaelian, Albert and Sun, Lixin and Geiger, Mario and Mailoa, Jonathan P. and Kornbluth, Mordechai and Molinari, Nicola and Smidt, Tess E. and Kozinsky, Boris , title=. Nat. Comm. , year=. doi:10.1038/s41467-022-29939-5 , url=

    work page doi:10.1038/s41467-022-29939-5

  18. [18]

    Learning local equivariant representations for large-scale atomistic dynamics,

    Musaelian, Albert and Batzner, Simon and Johansson, Anders and Sun, Lixin and Owen, Cameron J. and Kornbluth, Mordechai and Kozinsky, Boris , title=. Nat. Comm. , year=. doi:10.1038/s41467-023-36329-y , url=

    work page doi:10.1038/s41467-023-36329-y

  19. [19]

    A. P. Thompson and H. M. Aktulga and R. Berger and D. S. Bolintineanu and W. M. Brown and P. S. Crozier and P. J. in 't Veld and A. Kohlmeyer and S. G. Moore and T. D. Nguyen and R. Shan and M. J. Stevens and J. Tranchida and C. Trott and S. J. Plimpton. LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and con...

    work page doi:10.1016/j.cpc.2021.108171 2022

  20. [20]

    Michaud-Agrawal, E

    Michaud-Agrawal, Naveen and Denning, Elizabeth J. and Woolf, Thomas B. and Beckstein, Oliver , title =. J. Comput. Chem. , volume =. doi:https://doi.org/10.1002/jcc.21787 , year =

    work page doi:10.1002/jcc.21787

  21. [21]

    Self-Diffusivity and Viscosity from Equilibrium Molecular Dynamics [Article v1.0] , journal=

    Best Practices for Computing Transport Properties 1. Self-Diffusivity and Viscosity from Equilibrium Molecular Dynamics [Article v1.0] , journal=. 2018 , month=. doi:10.33011/livecoms.1.1.6324 , author=

    work page doi:10.33011/livecoms.1.1.6324 2018

  22. [22]

    Uberuaga, and Hannes Jónsson

    Henkelman, Graeme and Uberuaga, Blas P. and Jónsson, Hannes , title =. J. Chem. Phys. , volume =. 2000 , month =. doi:10.1063/1.1329672 , url =

    work page doi:10.1063/1.1329672 2000

  23. [23]

    VESTA : a three-dimensional visualization system for electronic and structural analysis

    Momma, Koichi and Izumi, Fujio. VESTA : a three-dimensional visualization system for electronic and structural analysis. J. Appl. Crystallogr. 2008. doi:10.1107/S0021889808012016 , url =

    work page doi:10.1107/s0021889808012016 2008

  24. [24]

    and Alvarez, Agustin O

    Schmidt, Moritz C. and Alvarez, Agustin O. and Pallotta, Riccardo and Seid, Biruk A. and de Boer, Jeroen J. and Thiesbrummel, Jarla and Lang, Felix and Grancini, Giulia and Ehrler, Bruno , title =. ACS Energy Lett. , volume =. 2026 , doi =

    2026

  25. [25]

    Quantification of ion migration in. Mater. Horiz. , author =. 2019 , pages =. doi:10.1039/C9MH00445A , language =

    work page doi:10.1039/c9mh00445a 2019

  26. [26]

    Ionic transport in hybrid lead iodide perovskite solar cells , volume =. Nat. Commun. , author =. 2015 , note =. doi:10.1038/ncomms8497 , language =

    work page doi:10.1038/ncomms8497 2015

  27. [27]

    Kinetics of. J. Am. Chem. Soc. , author =. 2015 , pages =. doi:10.1021/jacs.5b08535 , language =

    work page doi:10.1021/jacs.5b08535 2015

  28. [28]

    Native. Adv. Funct. Mater. , author =. 2016 , pages =. doi:10.1002/adfm.201504997 , language =

    work page doi:10.1002/adfm.201504997 2016

  29. [29]

    Iodine. Adv. Mater. , author =. 2016 , pages =. doi:10.1002/adma.201503832 , number =

    work page doi:10.1002/adma.201503832 2016

  30. [30]

    The. Angew. Chem. , author =. 2015 , pages =. doi:10.1002/anie.201500014 , language =

    work page doi:10.1002/anie.201500014 2015

  31. [31]

    Photovoltaic. Adv. Energy Mater. , author =. 2015 , pages =. doi:10.1002/aenm.201500615 , number =

    work page doi:10.1002/aenm.201500615 2015

  32. [32]

    Ultrafast ion migration in hybrid perovskite polycrystalline thin films under light and suppression in single crystals , volume =. Phys. Chem. Chem. Phys. , author =. 2016 , pages =. doi:10.1039/C6CP06496E , language =

    work page doi:10.1039/c6cp06496e 2016

  33. [33]

    Energy Environ

    Light-induced annihilation of. Energy Environ. Sci. , author =. 2016 , pages =. doi:10.1039/C6EE01504B , language =

    work page doi:10.1039/c6ee01504b 2016

  34. [34]

    Photo-induced halide redistribution in organic–inorganic perovskite films , volume =. Nat. Commun. , author =. 2016 , pages =. doi:10.1038/ncomms11683 , language =

    work page doi:10.1038/ncomms11683 2016

  35. [35]

    Reversible photo-induced trap formation in mixed-halide hybrid perovskites for photovoltaics , volume =. Chem. Sci. , author =. 2014 , pages =. doi:10.1039/C4SC03141E , language =

    work page doi:10.1039/c4sc03141e 2014

  36. [36]

    Ions. Adv. Funct. Mater. , author =. 2017 , pages =. doi:10.1002/adfm.201606584 , language =

    work page doi:10.1002/adfm.201606584 2017

  37. [37]

    Microseconds, milliseconds and seconds: deconvoluting the dynamic behaviour of planar perovskite solar cells , volume =. Phys. Chem. Chem. Phys. , author =. 2017 , pages =. doi:10.1039/C6CP08424A , language =

    work page doi:10.1039/c6cp08424a 2017

  38. [38]

    Joule , author =

    Influence of. Joule , author =. 2020 , pages =. doi:10.1016/j.joule.2020.01.012 , language =

    work page doi:10.1016/j.joule.2020.01.012 2020

  39. [39]

    Probing the ionic defect landscape in halide perovskite solar cells , volume =. Nat. Commun. , author =. 2020 , pages =. doi:10.1038/s41467-020-19769-8 , language =

    work page doi:10.1038/s41467-020-19769-8 2020

  40. [40]

    Quantifying mobile ions and electronic defects in perovskite-based devices with temperature-dependent capacitance measurements:. J. Chem. Phys. , author =. 2020 , pages =. doi:10.1063/1.5132754 , language =

    work page doi:10.1063/1.5132754 2020

  41. [41]

    Grain. J. Phys. Chem. Lett. , author =. 2021 , pages =. doi:10.1021/acs.jpclett.1c00205 , language =

    work page doi:10.1021/acs.jpclett.1c00205 2021

  42. [42]

    Haruyama, Jun and Sodeyama, Keitaro and Han, Liyuan and Tateyama, Yoshitaka , title =. J. Am. Chem. Soc. , volume =. 2015 , doi =

    2015

  43. [43]

    and Mosconi, Edoardo and Bisquert, Juan and De Angelis, Filippo

    Azpiroz, Jon M. and Mosconi, Edoardo and Bisquert, Juan and De Angelis, Filippo. Defect migration in methylammonium lead iodide and its role in perovskite solar cell operation. Energy Environ. Sci. 2015. doi:10.1039/C5EE01265A

    work page doi:10.1039/c5ee01265a 2015

  44. [44]

    Zhao, Chenyu and Cazorla, Claudio and Zhang, Xuliang and Huang, Hehe and Zhao, Xinyu and Li, Du and Shi, Junwei and Zhao, Qian and Ma, Wanli and Yuan, Jianyu , title =. J. Am. Chem. Soc. , volume =. 2024 , doi =

    2024

  45. [45]

    Crystal and electronic structures of substituted halide perovskites based on density functional calculation and molecular dynamics , author=. Chem. Phys. , volume=. 2017 , publisher=

    2017

  46. [46]

    Nano-Micro Lett

    Shen, Xiangqian and Lin, Xuesong and Su, Hongzhen and Zhang, Ziyang and Wu, Tianhao and Zhang, Jing and Peng, Yong and Zhang, Yiqiang and Zhang, Shufang and Zhou, Zhongmin and Meng, Xiangyue and Gao, Peng and Chen, Wei and Wu, Yongzhen and Qin, Chuanjiang and Han, Qifeng and Wang, Yanbo and Han, Liyuan , title=. Nano-Micro Lett. , year=. doi:10.1007/s4082...

    work page doi:10.1007/s40820-025-02022-6

  47. [47]

    and Röthlisberger, Ursula and Grätzel, Michael

    Yi, Chenyi and Luo, Jingshan and Meloni, Simone and Boziki, Ariadni and Ashari-Astani, Negar and Grätzel, Carole and Zakeeruddin, Shaik M. and Röthlisberger, Ursula and Grätzel, Michael. Entropic stabilization of mixed A-cation ABX3 metal halide perovskites for high performance perovskite solar cells. Energy Environ. Sci. 2016. doi:10.1039/C5EE03255E

    work page doi:10.1039/c5ee03255e 2016

  48. [48]

    , title =

    Bag, Santanu and Durstock, Michael F. , title =. ACS Appl. Mater. Interfaces , volume =. 2016 , doi =

    2016

  49. [49]

    npj Flex

    Wang, Feng and Bai, Sai and Tress, Wolfgang and Hagfeldt, Anders and Gao, Feng , title=. npj Flex. Electron. , year=. doi:10.1038/s41528-018-0035-z , url=

    work page doi:10.1038/s41528-018-0035-z

  50. [50]

    and Petrozza, Annamaria , title=

    Ball, James M. and Petrozza, Annamaria , title=. Nat. Energy , year=. doi:10.1038/nenergy.2016.149 , url=

    work page doi:10.1038/nenergy.2016.149 2016

  51. [51]

    Ion-induced field screening as a dominant factor in perovskite solar cell operational stability , journal=

    Thiesbrummel, Jarla and Shah, Sahil and Gutierrez-Partida, Emilio and Zu, Fengshuo and Pe. Ion-induced field screening as a dominant factor in perovskite solar cell operational stability , journal=. 2024 , month=. doi:10.1038/s41560-024-01487-w , url=

    work page doi:10.1038/s41560-024-01487-w 2024

  52. [52]

    ACS Appl

    Apergi, Sofia and Koch, Christine and Brocks, Geert and Olthof, Selina and Tao, Shuxia , title =. ACS Appl. Mater. Interfaces , volume =. 2022 , doi =

    2022

  53. [53]

    ACS Appl

    Apergi, Sofia and Brocks, Geert and Tao, Shuxia and Olthof, Selina , title =. ACS Appl. Mater. Interfaces , volume =. 2024 , doi =

    2024

  54. [54]

    Semerci, Ali and Urieta-Mora, Javier and Driessen, Sander and Buyruk, Ali and Hooijer, Rik and Molina-Ontoria, Agustín and Alkan, Bülent and Akin, Seckin and Fanetti, Mattia and Balakrishnan, Harishankar and Hartschuh, Achim and Tao, Shuxia and Martín, Nazario and Müller-Buschbaum, Peter and Emin, Saim and Ameri, Tayebeh , title =. Adv. Funct. Mater. , vo...

    work page doi:10.1002/adfm.202423109

  55. [55]

    How crystallization additives govern halide perovskite grain growth , journal=

    Maschwitz, Timo and Merten, Lena and. How crystallization additives govern halide perovskite grain growth , journal=. 2025 , month=. doi:10.1038/s41467-025-65484-7 , url=

    work page doi:10.1038/s41467-025-65484-7 2025

  56. [56]

    Compound Defects in Halide Perovskites: A First-Principles Study of CsPbI3 , journal =

    Xue, Haibo and Vicent-Luna, Jos. Compound Defects in Halide Perovskites: A First-Principles Study of CsPbI3 , journal =. 2023 , doi =

    2023

  57. [57]

    Ion migration in perovskite solar cells , journal=

    Thiesbrummel, Jarla and Mili. Ion migration in perovskite solar cells , journal=. 2026 , month=. doi:10.1038/s41570-025-00790-8 , url=

    work page doi:10.1038/s41570-025-00790-8 2026

  58. [58]

    and Mann, Jennifer E

    Clark, Catherine P. and Mann, Jennifer E. and Bangsund, John S. and Hsu, Wan-Ju and Aydil, Eray S. and Holmes, Russell J. , title =. ACS Energy Lett. , volume =. 2020 , doi =

    2020

  59. [59]

    Finite-temperature structure of the

    Lahnsteiner, Jonathan and Kresse, Georg and Heinen, Jurn and Bokdam, Menno , journal =. Finite-temperature structure of the. 2018 , month =

    2018

  60. [60]

    Pazoki and M.J

    M. Pazoki and M.J. Wolf and T. Edvinsson and J. Kullgren , keywords =. Vacancy dipole interactions and the correlation with monovalent cation dependent ion movement in lead halide perovskite solar cell materials , journal =. 2017 , issn =. doi:https://doi.org/10.1016/j.nanoen.2017.06.024 , url =

    work page doi:10.1016/j.nanoen.2017.06.024 2017

  61. [61]

    and Pering, Samuel R

    Ferdani, Dominic W. and Pering, Samuel R. and Ghosh, Dibyajyoti and Kubiak, Peter and Walker, Alison B. and Lewis, Simon E. and Johnson, Andrew L. and Baker, Peter J. and Islam, M. Saiful and Cameron, Petra J. Partial cation substitution reduces iodide ion transport in lead iodide perovskite solar cells. Energy Environ. Sci. 2019. doi:10.1039/C9EE00476A

    work page doi:10.1039/c9ee00476a 2019

  62. [62]

    Woo, Young Won and Jung, Young-Kwang and Kim, Gee Yeong and Kim, Sunghyun and Walsh, Aron , title=. Discov. Mater. , year=. doi:10.1007/s43939-022-00029-z , url=

    work page doi:10.1007/s43939-022-00029-z

  63. [63]

    Intrinsic defects in primary halide perovskites: A first-principles study of the thermodynamic trends , author =. Phys. Rev. Mater. , volume =. 2022 , month =. doi:10.1103/PhysRevMaterials.6.055402 , url =

    work page doi:10.1103/physrevmaterials.6.055402 2022

  64. [64]

    and Caddeo, C

    Delugas, P. and Caddeo, C. and Filippetti, A. and Mattoni, A. , title =. J. Phys. Chem. Lett. , volume =. 2016 , doi =

    2016

  65. [65]

    Balestra, Salvador R. G. and Vicent-Luna, Jose Manuel and Calero, Sofia and Tao, Shuxia and Anta, Juan A. Efficient modelling of ion structure and dynamics in inorganic metal halide perovskites. J. Mater. Chem. A. 2020. doi:10.1039/D0TA03200J

    work page doi:10.1039/d0ta03200j 2020

  66. [66]

    Four generations of high-dimensional neural network potentials

    Behler, J \"o rg. Four generations of high-dimensional neural network potentials. Chem. Rev

  67. [67]

    and Chmiela, Stefan and Sauceda, Huziel E

    Unke, Oliver T. and Chmiela, Stefan and Sauceda, Huziel E. and Gastegger, Michael and Poltavsky, Igor and Sch. Machine Learning Force Fields , journal =. 2021 , doi =

    2021

  68. [68]

    Wu, Shiru and Yang, Xiaowei and Zhao, Xun and Li, Zhipu and Lu, Min and Xie, Xiaoji and Yan, Jiaxu , title =. J. Chem. Inf. Model. , volume =. 2023 , doi =

    2023

  69. [69]

    Point defect formation at finite temperatures with machine learning force fields

    Mosquera-Lois, Irea and Klarbring, Johan and Walsh, Aron. Point defect formation at finite temperatures with machine learning force fields. Chem. Sci. 2025. doi:10.1039/D4SC08582E

    work page doi:10.1039/d4sc08582e 2025

  70. [70]

    Tyagi, Viren and Pols, Mike and Brocks, Geert and Tao, Shuxia , title =. Chem. Mater. , year =

  71. [71]

    ACS Energy Lett

    Meggiolaro, Daniele and De Angelis, Filippo , title =. ACS Energy Lett. , volume =. 2018 , doi =

    2018

  72. [72]

    Ni, Zhenyi and Jiao, Haoyang and Fei, Chengbin and Gu, Hangyu and Xu, Shuang and Yu, Zhenhua and Yang, Guang and Deng, Yehao and Jiang, Qi and Liu, Ye and Yan, Yanfa and Huang, Jinsong , title=. Nat. Energy , year=. doi:10.1038/s41560-021-00949-9 , url=

    work page doi:10.1038/s41560-021-00949-9

  73. [73]

    and Meggiolaro, Daniele and Barker, Alex J

    Motti, Silvia G. and Meggiolaro, Daniele and Barker, Alex J. and Mosconi, Edoardo and Perini, Carlo Andrea Riccardo and Ball, James M. and Gandini, Marina and Kim, Min and De Angelis, Filippo and Petrozza, Annamaria , title=. Nat. Photonics , year=. doi:10.1038/s41566-019-0435-1 , url=

    work page doi:10.1038/s41566-019-0435-1

  74. [74]

    Toolsets for assessing ionic migration in halide perovskites , journal =

    Natalia Yantara and Nripan Mathews , keywords =. Toolsets for assessing ionic migration in halide perovskites , journal =. 2024 , issn =. doi:https://doi.org/10.1016/j.joule.2024.02.022 , url =

    work page doi:10.1016/j.joule.2024.02.022 2024

  75. [75]

    and Alvarez, Agustin O

    Schmidt, Moritz C. and Alvarez, Agustin O. and de Boer, Jeroen J. and van de Ven, Larissa J.M. and Ehrler, Bruno , title =. ACS Energy Lett. , volume =. 2024 , doi =

    2024

  76. [76]

    doi:10.5281/zenodo.20052556 , url =

    Tyagi, Viren , title =. doi:10.5281/zenodo.20052556 , url =

    work page doi:10.5281/zenodo.20052556